# std::asinh, std::asinhf, std::asinhl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float asinh ( float num ); double asinh ( double num ); long double asinh ( long double num ); |  | (until C++23)
/*floating-point-type*/ asinh ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float asinhf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double asinhl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> asinh ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double asinh ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the inverse hyperbolic sine of num. The library provides overloads of `std::asinh` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::asinh` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the inverse hyperbolic sine of num (sinh-1
(num), or arsinh(num)), is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is ±0 or ±∞, it is returned unmodified.
- if the argument is NaN, NaN is returned.

### Notes

Although the C standard (to which C++ refers for this function) names this function "arc hyperbolic sine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic sine" (used by POSIX) or "area hyperbolic sine".

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::asinh(num) has the same effect as std::asinh(static_cast<double>(num)).

### Examples

Run this code

    #include <cmath>
    #include <iostream>

    int main()
    {
        std::cout << "asinh(1) = " << std::asinh(1) << '\n'
                  << "asinh(-1) = " << std::asinh(-1) << '\n';

        // special values
        std::cout << "asinh(+0) = " << std::asinh(+0.0) << '\n'
                  << "asinh(-0) = " <<  std::asinh(-0.0) << '\n';
    }

Output:

    asinh(1) = 0.881374
    asinh(-1) = -0.881374
    asinh(+0) = 0
    asinh(-0) = -0

### See also

acoshacoshfacoshl (C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)artanh(x)) (function)
sinhsinhfsinhl (C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x)) (function)
asinh(std::complex) (C++11) | computes area hyperbolic sine of a complex number (\({\small\operatorname{arsinh}{z}}\)arsinh(z)) (function template)
C documentation for asinh

### External links

Weisstein, Eric W. "Inverse Hyperbolic Sine." From MathWorld — A Wolfram Web Resource.

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